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Simplifying 15x2 + 10x + -3 = 0 Reorder the terms: -3 + 10x + 15x2 = 0 Solving -3 + 10x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.2 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 0.6666666667x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 0.6666666667x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.6666666667x + x2 = 0 + 0.2 0.6666666667x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 0.6666666667x + x2 = 0.2 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 0.2 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 0.2 + 0.1111111112 Combine like terms: 0.2 + 0.1111111112 = 0.3111111112 0.1111111112 + 0.6666666667x + x2 = 0.3111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.3111111112 Calculate the square root of the right side: 0.557773351 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.557773351 and -0.557773351.Subproblem 1
x + 0.3333333334 = 0.557773351 Simplifying x + 0.3333333334 = 0.557773351 Reorder the terms: 0.3333333334 + x = 0.557773351 Solving 0.3333333334 + x = 0.557773351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 0.557773351 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.557773351 + -0.3333333334 x = 0.557773351 + -0.3333333334 Combine like terms: 0.557773351 + -0.3333333334 = 0.2244400176 x = 0.2244400176 Simplifying x = 0.2244400176Subproblem 2
x + 0.3333333334 = -0.557773351 Simplifying x + 0.3333333334 = -0.557773351 Reorder the terms: 0.3333333334 + x = -0.557773351 Solving 0.3333333334 + x = -0.557773351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -0.557773351 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.557773351 + -0.3333333334 x = -0.557773351 + -0.3333333334 Combine like terms: -0.557773351 + -0.3333333334 = -0.8911066844 x = -0.8911066844 Simplifying x = -0.8911066844Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2244400176, -0.8911066844}
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